Chapter 5, Problem 5.17P

Interpretation Introduction

Interpretation: The axial stress at junctions $1\text{and}2$ is to be calculated.

Concept introduction:

The axial stress is the stress that causes the change in length of the body in the direction of applied force.

In the other words stress is the force per unit area. To calculate the stress at junctions $1\text{and}2$ , the force should be calculated. The given system is of varying cross section and different value of pressure at corresponding junctions.

To calculate the force in a varying cross section, the momentum balance is applied.

According to the momentum balance equation, the summation of the forces acting on the body is balanced by the rate of change of momentum.

The momentum balance equation for control volumeis,

  ${\displaystyle \sum F_x}={\displaystyle \underset{c.s}{\iint }{v}_x\rho \left(\overrightarrow{v}\cdot \overrightarrow{n}\right)}dA$